We report on the crystal structure and magnetism of the iron-based oxyfluoride Bi4Fe5O13F, a material prototype of the Cairo pentagonal spin lattice. The crystal structure of Bi4Fe5O13F is determined by a combination of neutron diffraction, synchrotron x-ray diffraction, and transmission electron microscopy. It comprises layers of FeO6 octahedra and FeO4 tetrahedra forming deformed pentagonal units. The topology of these layers resembles a pentagonal least-perimeter tiling, which is known as the Cairo lattice. This topology gives rise to frustrated exchange couplings and underlies a sequence of magnetic transitions at T-1 = 62 K, T-2 = 71 K, and T-N = 178 K, as determined by thermodynamic measurements and neutron diffraction. Below T-1, Bi4Fe5O13F forms a fully ordered non-collinear antiferromagnetic structure, whereas the magnetic state between T-1 and T-N may be partially disordered according to the sizable increase in the magnetic entropy at T-1 and T-2. Bi4Fe5O13F reveals unanticipated magnetic transitions on the pentagonal Cairo spin lattice and calls for a further work on finite-temperature properties of this strongly frustrated spin model. DOI: 10.1103/PhysRevB.87.024423